This is a very loaded question, and depends on your company to be sure. I first have to ask, why are you using 3 environments and continuous integration (your reason matters)? Are you performing automated tests at all? How are your code branches setup? Do you release for some functionality, or just routine maintenance fixes?
Answering these will give you an idea of why you need a release, and how you should go about it.
For example, if you only have a staging environment for the purpose of integration and perform automated tests, then can't having a separate code branch in which continuous integration tests run be sufficient?
If staging is to perform some sort of user acceptance, does your company have a dedicated testing team or are they members of the agile teams?
As you correctly stated, if the code is always integrated and tested, then why would you need a timetable and moving from environment to environment unless you were unsure about the actual "done" condition of the features? By that, I mean that it's not that you're unsure that the feature was coded correctly, but are you worried it will introduce other bugs? Will it integrate well with code already in production? Address the concerns at the root of the problem. Don't just do it because you think you're supposed to have X environments or testing should be in another group. Maybe the solutions to those problems may be to adjust the definition of "done" accordingly.
As you can see there are many, many factors that will make your organization unique. There is no one right way to answer this, just tradeoffs that you are willing to accept.
I find that having multiple environments with teams of people working at the various layers tends to be anti-agile and counterproductive. The best bet is to analyze your concerns, and try to find ways to solve them (such as expanding the definition of "done", or breaking up the various organizations and putting them on the teams, eliminating as many environments as possible and simplifying the process, etc). That may not be possible in your organization, so you may have to live with tradeoffs.